The lamp of a streetlight is 12 feet above the street below. a girl, who is 5 feet tall stands at a point 6 feet from the spot directly below the light. how long is her shadow?

The image attached shows a diagram of the problem. 
We first want to find the angle, or rather the tangent of the angle, formed by the light, the pole, and the ray of light that travels across the girl's noggin to the tip of her shadow:

tan (x) = opposite/ adjacent
tan (x) = 6 / 7
We know that the tangeant of this angle is 6/7

We can then apply this ratio to the total length from the pole to her shadow:
6/7 = x / 12        Cross multiply
7x = 72
x = 72/7 = 10.29

The total length from the base of the pole to her shadow is 10.29 feet. 
She is 6 feet from the pole, so her shadow is:
10.29 - 6 = 4.29 feet long